1,056 research outputs found
Interplay of frequency-synchronization with noise: current resonances, giant diffusion and diffusion-crests
We elucidate how the presence of noise may significantly interact with the
synchronization mechanism of systems exhibiting frequency-locking. The response
of these systems exhibits a rich variety of behaviors, such as resonances and
anti-resonances which can be controlled by the intensity of noise. The
transition between different locked regimes provokes the development of a
multiple enhancement of the effective diffusion. This diffusion behavior is
accompanied by a crest-like peak-splitting cascade when the distribution of the
lockings is self-similar, as it occurs in periodic systems that are able to
exhibit a Devil's staircase sequence of frequency-lockings.Comment: 7 pages, 6 figures, epl.cls. Accepted for publication in Europhysics
Letter
Cooperative surmounting of bottlenecks
The physics of activated escape of objects out of a metastable state plays a
key role in diverse scientific areas involving chemical kinetics, diffusion and
dislocation motion in solids, nucleation, electrical transport, motion of flux
lines superconductors, charge density waves, and transport processes of
macromolecules, to name but a few. The underlying activated processes present
the multidimensional extension of the Kramers problem of a single Brownian
particle. In comparison to the latter case, however, the dynamics ensuing from
the interactions of many coupled units can lead to intriguing novel phenomena
that are not present when only a single degree of freedom is involved. In this
review we report on a variety of such phenomena that are exhibited by systems
consisting of chains of interacting units in the presence of potential
barriers.
In the first part we consider recent developments in the case of a
deterministic dynamics driving cooperative escape processes of coupled
nonlinear units out of metastable states. The ability of chains of coupled
units to undergo spontaneous conformational transitions can lead to a
self-organised escape. The mechanism at work is that the energies of the units
become re-arranged, while keeping the total energy conserved, in forming
localised energy modes that in turn trigger the cooperative escape. We present
scenarios of significantly enhanced noise-free escape rates if compared to the
noise-assisted case.
The second part deals with the collective directed transport of systems of
interacting particles overcoming energetic barriers in periodic potential
landscapes. Escape processes in both time-homogeneous and time-dependent driven
systems are considered for the emergence of directed motion. It is shown that
ballistic channels immersed in the associated high-dimensional phase space are
the source for the directed long-range transport
Entropic stochastic resonance: the constructive role of the unevenness
We demonstrate the existence of stochastic resonance (SR) in confined systems
arising from entropy variations associated to the presence of irregular
boundaries. When the motion of a Brownian particle is constrained to a region
with uneven boundaries, the presence of a periodic input may give rise to a
peak in the spectral amplification factor and therefore to the appearance of
the SR phenomenon. We have proved that the amplification factor depends on the
shape of the region through which the particle moves and that by adjusting its
characteristic geometric parameters one may optimize the response of the
system. The situation in which the appearance of such entropic stochastic
resonance (ESR) occurs is common for small-scale systems in which confinement
and noise play an prominent role. The novel mechanism found could thus
constitute an important tool for the characterization of these systems and can
put to use for controlling their basic properties.Comment: 8 pages, 8 figure
Non-Markovian Stochastic Resonance
The phenomenological linear response theory of non-Markovian Stochastic
Resonance (SR) is put forward for stationary two-state renewal processes. In
terms of a derivation of a non-Markov regression theorem we evaluate the
characteristic SR-quantifiers; i.e. the spectral power amplification (SPA) and
the signal-to-noise ratio (SNR), respectively. In clear contrast to Markovian
SR, a characteristic benchmark of genuine non-Markovian SR is its distinctive
dependence of the SPA and SNR on small (adiabatic) driving frequencies;
particularly, the adiabatic SNR becomes strongly suppressed over its Markovian
counterpart. This non-Markovian SR theory is elucidated for a fractal gating
dynamics of a potassium ion channel possessing an infinite variance of closed
sojourn times.Comment: 4 pages, 1 figur
The charge shuttle as a nanomechanical ratchet
We consider the charge shuttle proposed by Gorelik {\em et al.} driven by a
time-dependent voltage bias. In the case of asymmetric setup, the system
behaves as a rachet. For pure AC drive, the rectified current shows a complex
frequency dependent response characterized by frequency locking at fracional
values of the external frequency. Due to the non-linear dynamics of the
shuttle, the rachet effect is present also for very low frequencies.Comment: 4 pages, 4 figure
Anomalous diffusion for overdamped particles driven by cross-correlated white noise sources
We study the statistical properties of overdamped particles driven by two
cross-correlated multiplicative Gaussian white noises in a time-dependent
environment. Using the Langevin and Fokker-Planck approaches, we derive the
exact probability distribution function for the particle positions, calculate
its moments and find their corresponding long-time, asymptotic behaviors. The
generally anomalous diffusive regimes of the particles are classified, and
their dependence on the friction coefficient and the characteristics of the
noises is analyzed in detail. The asymptotic predictions are confirmed by exact
solutions for two examples.Comment: 15 page
The Third Law of Quantum Thermodynamics in the Presence of Anomalous Couplings
The quantum thermodynamic functions of a harmonic oscillator coupled to a
heat bath through velocity-dependent coupling are obtained analytically. It is
shown that both the free energy and the entropy decay fast with the temperature
in relation to that of the usual coupling from. This implies that the
velocity-dependent coupling helps to ensure the third law of thermodynamics.Comment: 4 pages, 3 figures, 22 conference
Capacitance fluctuations causing channel noise reduction in stochastic Hodgkin-Huxley systems
Voltage-dependent ion channels determine the electric properties of axonal
cell membranes. They not only allow the passage of ions through the cell
membrane but also contribute to an additional charging of the cell membrane
resulting in the so-called capacitance loading. The switching of the channel
gates between an open and a closed configuration is intrinsically related to
the movement of gating charge within the cell membrane. At the beginning of an
action potential the transient gating current is opposite to the direction of
the current of sodium ions through the membrane. Therefore, the excitability is
expected to become reduced due to the influence of a gating current. Our
stochastic Hodgkin-Huxley like modeling takes into account both the channel
noise -- i.e. the fluctuations of the number of open ion channels -- and the
capacitance fluctuations that result from the dynamics of the gating charge. We
investigate the spiking dynamics of membrane patches of variable size and
analyze the statistics of the spontaneous spiking. As a main result, we find
that the gating currents yield a drastic reduction of the spontaneous spiking
rate for sufficiently large ion channel clusters. Consequently, this
demonstrates a prominent mechanism for channel noise reduction.Comment: 18 page
Theory of the Relativistic Brownian Motion. The (1+1)-Dimensional Case
We construct a theory for the 1+1-dimensional Brownian motion in a viscous
medium, which is (i) consistent with Einstein's theory of special relativity,
and (ii) reduces to the standard Brownian motion in the Newtonian limit case.
In the first part of this work the classical Langevin equations of motion,
governing the nonrelativistic dynamics of a free Brownian particle in the
presence of a heat bath (white noise), are generalized in the framework of
special relativity. Subsequently, the corresponding relativistic Langevin
equations are discussed in the context of the generalized Ito (pre-point
discretization rule) vs. the Stratonovich (mid-point discretization rule)
dilemma: It is found that the relativistic Langevin equation in the
Haenggi-Klimontovich interpretation (with the post-point discretization rule)
is the only one that yields agreement with the relativistic Maxwell
distribution. Numerical results for the relativistic Langevin equation of a
free Brownian particle are presented.Comment: see cond-mat/0607082 for an improved theor
Microcanonical quantum fluctuation theorems
Previously derived expressions for the characteristic function of work
performed on a quantum system by a classical external force are generalized to
arbitrary initial states of the considered system and to Hamiltonians with
degenerate spectra. In the particular case of microcanonical initial states
explicit expressions for the characteristic function and the corresponding
probability density of work are formulated. Their classical limit as well as
their relations to the respective canonical expressions are discussed. A
fluctuation theorem is derived that expresses the ratio of probabilities of
work for a process and its time reversal to the ratio of densities of states of
the microcanonical equilibrium systems with corresponding initial and final
Hamiltonians.From this Crooks-type fluctuation theorem a relation between
entropies of different systems can be derived which does not involve the time
reversed process. This entropy-from-work theorem provides an experimentally
accessible way to measure entropies.Comment: revised and extended versio
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